Algebra Examples

${(\frac{{(4 x^{2} y^{3})}^{0}}{- 3 x^{- 1} y^{2}})}^{3}$

Step 1

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{{(4 x^{2} y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $4 x^{2} y^{3}$ .

${(\frac{{(4 x^{2})}^{0} {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.2

Apply the product rule to $4 x^{2}$ .

${(\frac{4^{0} {(x^{2})}^{0} {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.3

Anything raised to $0$ is $1$ .

${(\frac{1 {(x^{2})}^{0} {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.4

Multiply ${(x^{2})}^{0}$ by $1$ .

${(\frac{{(x^{2})}^{0} {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.5

Multiply the exponents in ${(x^{2})}^{0}$ .

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Step 2.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{x^{2 \cdot 0} {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.5.2

Multiply $2$ by $0$ .

${(\frac{x^{0} {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.6

Anything raised to $0$ is $1$ .

${(\frac{1 {(y^{3})}^{0} x}{- 3 y^{2}})}^{3}$

Step 2.7

Multiply the exponents in ${(y^{3})}^{0}$ .

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Step 2.7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(\frac{1 y^{3 \cdot 0} x}{- 3 y^{2}})}^{3}$

Step 2.7.2

Multiply $3$ by $0$ .

${(\frac{1 y^{0} x}{- 3 y^{2}})}^{3}$

Step 2.8

Anything raised to $0$ is $1$ .

${(\frac{1 \cdot 1 x}{- 3 y^{2}})}^{3}$

Step 2.9

Combine exponents.

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Step 2.9.1

Multiply $1$ by $1$ .

${(\frac{1 x}{- 3 y^{2}})}^{3}$

Step 2.9.2

Multiply $x$ by $1$ .

${(\frac{x}{- 3 y^{2}})}^{3}$

Step 3

Move the negative in front of the fraction.

${(- \frac{x}{3 y^{2}})}^{3}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $- \frac{x}{3 y^{2}}$ .

${(- 1)}^{3} {(\frac{x}{3 y^{2}})}^{3}$

Step 4.2

Apply the product rule to $\frac{x}{3 y^{2}}$ .

${(- 1)}^{3} \frac{x^{3}}{{(3 y^{2})}^{3}}$

Step 4.3

Apply the product rule to $3 y^{2}$ .

${(- 1)}^{3} \frac{x^{3}}{3^{3} {(y^{2})}^{3}}$

Step 5

Raise $- 1$ to the power of $3$ .

$- \frac{x^{3}}{3^{3} {(y^{2})}^{3}}$

Step 6

Simplify the denominator.

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Step 6.1

Raise $3$ to the power of $3$ .

$- \frac{x^{3}}{27 {(y^{2})}^{3}}$

Step 6.2

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 6.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{x^{3}}{27 y^{2 \cdot 3}}$

Step 6.2.2

Multiply $2$ by $3$ .

$- \frac{x^{3}}{27 y^{6}}$